For reasons of efficiency, ease of implementation and noise reduction, it has been suggested that an analog-to-digital converter include an input stage in which the analog signal is converted to a coarsely quantized digital representation at a sample rate many times greater than the Nyquist rate. Thereafter, the digital representation is "decimated" by combining groups of high rate samples into corresponding digital values which occur at the desired slower rate. This output may then be used directly, or filtered further prior to application to a utilization device. A general description of oversampled A/D encoding, and its features and advantages, is contained in an article by D. J. Goodman entitled "The Application of Delta Modulation to Analog-to-Digital PCM Encoding", Bell System Technical Journal, Vol. 48, February 1969, pp. 321-343.
In the decimation process described above, due care must be taken to reduce or eliminate the noise (distortion) introduced during the coarse quantization, and to avoid aliasing by which noise is introduced into the final digital signal during subsequent processing. One technique for decimation filtering is a unique weighted accumulation procedure described in U.S. Pat. No. 4,032,914 issued to J. C. Candy and Y. Ching (Candy being one of the inventors herein) on June 28, 1977. In that patent, the m coarsely quantized sample values for each desired output sample interval are combined using triangular or trapezoidal weighting. By this, it is meant that sample values near the beginning and end of the interval are given lower weight, relative to value, near the middle of the interval. Thus, in triangular weighting for m=8 samples X.sub.0, X.sub.1. . . X.sub.7, a summation might be taken such that the output is proportional to 0X.sub.0 +1X.sub.1 +X.sub.2 +3X.sub.3 +4X.sub.4 +3X.sub.5 +2X.sub.6 +1X.sub.7. In trapezoidally weighted accumulation, the same eight samples might be weighted such that the output varies with 0.sub.X.sub.0 +1X.sub.1 +2X.sub.2 +3X.sub.3 +3X.sub.4 +3X.sub.5 +2X.sub.6 + 1X.sub.7. If the coefficient values are plotted against time for the two examples given, the first would form a triangle and the second a trapezoid.
The technique just described, implemented using a serially connected pair of accumulators, is somewhat successful in reducing quantizing noise, as desired. However, aliasing effects still persist, to a degree, and the frequency response characteristic of the circuit does not meet all system requirements. Accordingly, it is the broad object of the present invention to provide an improved digital-to-digital converter or decimator having desired transfer characteristics. Specific objects include reduction in aliasing and simplification of circuit implementation, particularly using integrated circuit fabrication techniques.